Am I exempted from making quartely estimated payments on my current year income 1099-MISC?

I was out of the USA for whole year 2017. I returned to the USA in 2018 and filed foreign earned income exclusion form 2225-EZ along with 1040, 1040 SB, etc. So I did not have to pay any taxes. It came up to be $0 for Federal & State both.

Now, I am working as a Postdoctoral Fellow and my offer letter says, "Stipend payments are recognized by the IRS as “Miscellaneous Income – Prizes and Awards” as defined in IRS Code Section 74. The participant is advised to identify their payments as “Other Income” and as being a “Fellowship Award”."

My questions is:

Do I need to make quarterly estimated payments for my current year 2018 income or I am exempted as I had no tax liability/$0 tax last year 2017 due to foreign earned income exclusion?

If I am exempted, does it mean, that I can pay all taxes at once in year 2019 when I receive 1099-MISC?

You don’t owe a penalty if you had no tax liability last year and you were a U.S. citizen or resident for the whole year. For this rule to apply, your tax year must have included all 12 months of the year.

You had no tax liability for 2016 if your total tax was zero or you were not required to file an income tax return.

Example.

Ray, who is single and 22 years old, was unemployed for a few months during 2016. He earned $6,700 in wages before he was laid off, and he received $1,400 in unemployment compensation afterwards. He had no other income. Even though he had gross income of $8,100, he didn’t have to pay income tax because his gross income was less than the filing requirement for a single person under age 65 ($10,350 for 2016). He filed a return only to have his withheld income tax refunded to him.

In 2017, Ray began regular work as an independent contractor. Ray made no estimated tax payments in 2017. Even though he did owe tax at the end of the year, Ray does not owe the underpayment penalty for 2017 because he had no tax liability in 2016.